ON THE STABILITY OF THE CUBIC FUNCTIONAL EQUATION IN TOPOLOGICAL VECTOR SPACES

In this paper we investigate the Hyers-Ulam stability of the following functional equation: kf(kx + y) + kf(kx ¡ y) = kg(kx + y) + kg(kx ¡ y) + 2g(kx) ¡ 2kg(x) in topological vector spaces, where f; g are functions defined on a group with values in a topological vector spaces.